Question

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

90

170

126

91

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

x =	thousand dollars
s =	thousand dollars

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

Answer 1

SOLUTION:

From given data,

90

170

126

91

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s.

sample mean = = x / n = (90+170+126+91+75+94+116+100+85) / 9 = 947/9 = 105.22

= $ 105.2 (Round your answers to one decimal place.)

sample standard deviation = s = sqrt( (x-)^2 / (n-1) )

s = sqrt(( (90-105.22)^2+(170-105.22)^2+(126-105.22)^2+(91-105.22)^2+(75-105.22)^2+(94-105.22)^2+(116-105.22)^2+(100-105.22)^2+(85-105.22)^2 ) / (9-1) )

s = sqrt(6653.5556/8)

s = 28.839113

s = $ 28.8 (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises.

90% confidence interval

c = 90% = 90/100 = 0.90

= 1-c = 1-0.90 = 0.1

/2 = 0.1/2 = 0.05

Degree of freedom = df = n-1 = 9-1 = 8

critical value = t_c = t_/2,df = t_0.05,8 = 1.86

Margin of error = E = t_c * (s/sqrt(n))

E = 1.86 * (28.8 /sqrt(9))

E = 1.86 * 9.6

E = 17.856

lower limit = - E = 105.2 - 17.856 = 87.344 = $ 87.3 (Round your answers to one decimal place.)

upper limit =   + E =105.2+17.856 =123.056 = $123.1(Round your answers to one decimal place.)

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